We use Intuit Go Payment. We stopped using square because of how the transaction came into our bank account. It throws off quickbooks. Square takes the money out before they deposit it to your account. If you want to keep your books balanced correctly avoid using square. With the Go Payment, the full amount is deposited, and then a separate transaction is done where they take their merchant fees.
Why can't you record it in Quickbooks the same way for Square?
Just apply the full payment to the customer's invoice, then when making the deposit in QB, add a line for Square with a negative amount for the merchant account fees, and the deposit should equal Square's deposit amount.
That's how I do it, anyhow.